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I am creating composites of a host epoxy and filler particles which are thin-walled fluid-filled shells. Using the Halpin-Tsai equations, for example, I can predict the bulk composite Young's modulus by knowing the particle volume fraction, modulus, geometry, etc, and this seems to work well for both Solid and Liquid particles (using a negligible modulus to approximate liquid)

However, I am having difficulty determining the effective modulus of a liquid-core shell particle for use in these equations. I have found this paper Bulk Modulus of a fluid-filled spherical shell which provides a formula to predict the Bulk Modulus of such a shell, but without also knowing the Shear Modulus or Poisson's Ratio of these fluid-filled shells I cannot determine a Young's Modulus.

This seems like something that should have a well-documented formula, but I can't seem to find anything. Any ideas on how to calculate the Young's Modulus?

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  • $\begingroup$ Why not load it and then determine the value. $\endgroup$
    – Solar Mike
    Dec 2 '20 at 21:17
  • $\begingroup$ We have experimental data for the composite as a whole, but measuring the stress for individual microparticles is out of the range of our equipment. The composite measurements are showing behavior that does not match typical model predictions that assume a fully solid particle or fully liquid particle, so the reason we want a shell analytical model is to verify our hypothesis that it is the shell itself causing the unusual behavior, and which one would then let us tune shell thickness to achieve desired results. $\endgroup$ Dec 3 '20 at 14:07

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